We present the continuous state vector of the total coordinate of multi-partlcle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of th...We present the continuous state vector of the total coordinate of multi-partlcle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product （IWOP） technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.展开更多
We mostly investigate two schemes. One is to teleport a multi-mode W-type entangled coherent state using a peculiar bipartite entangled state as the quantum channel different from other proposals. Based on our formali...We mostly investigate two schemes. One is to teleport a multi-mode W-type entangled coherent state using a peculiar bipartite entangled state as the quantum channel different from other proposals. Based on our formalism,teleporting multi-mode coherent state or squeezed state is also possible. Another is that the tripartite entangled state is used as the quantum channel of controlled teleportation of an arbitrary and unknown continuous variable in the case of three participators.展开更多
This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state repre...This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state representations seem to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.展开更多
With the help of Bose operator identities and entangled state representation and based on our previous work.[Phys. Lett. A 325 （2004） 188] we derive some new generalized Bessel equations which also have Bessel funct...With the help of Bose operator identities and entangled state representation and based on our previous work.[Phys. Lett. A 325 （2004） 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.展开更多
Based on the fact that the quantum mechanical version of Hankel transform kernel（the Bessel function） is just the transform between ｜q, r〉 and（s, r′｜, two induced entangled state representations are given, and ...Based on the fact that the quantum mechanical version of Hankel transform kernel（the Bessel function） is just the transform between ｜q, r〉 and（s, r′｜, two induced entangled state representations are given, and working with them we derive fractional squeezing-Hankel transform（FrSHT） caused by the operator e（-iα）（a1-a-2-＋a-1a-2）e-（-iπa2-a2）, which is an entangled fractional squeezing transform operator. The additive rule of the FrSHT can be explicitly proved.展开更多
Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, wesolve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum rep...Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, wesolve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum representation ofits analytical solution. we find that the pure coherent states evolve into the new mixed thermal superposed states in thediffusion channel. Also, we investigate the statistical properties of the initial coherent states and their entropy evolutions inthe diffusion channel, and find that the entropy evolutions are only related to the decay time and without the amplitudes ofthe initial coherent states.展开更多
To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive t...To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.展开更多
By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation （η｜, which can arrange master equations of density operators p（t） in quant...By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation （η｜, which can arrange master equations of density operators p（t） in quantum statistics as state-vector evolution equations due to the elegant properties of （η｜. In this way many master equations （respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators） can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p（t） at time t in 〈η｜ representation is proportional to that of the initial po in the decayed entangled state （ηe^-kt｜ representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f（d^2η/π）（η｜ρ〉D（η）, which is different from all the previous known representations.展开更多
Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum represent...Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.展开更多
For the first time we derive the evolution law of the negative binomial state In） （nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state ...For the first time we derive the evolution law of the negative binomial state In） （nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.展开更多
By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. Th...By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. The technique of integration within an ordered product （IWOP） of operators is employed in our discussions.展开更多
This paper introduces a new concept of ＂State Representation Methodology （SRM）＂ which is a kind of bridge condition assessment method for structural health monitoring system （SHM）. There are many methods for sys...This paper introduces a new concept of ＂State Representation Methodology （SRM）＂ which is a kind of bridge condition assessment method for structural health monitoring system （SHM）. There are many methods for system identification from the simplicity comparison of damage index to the complicated statistical pattern recognition algorithms in SHM. In these methods, modal analysis and parameters identification or many defined indices are common-used for extracting the dynamic or static characteristics of a system. However, there is a common problem： due to the complexity of a large size system with high-order nonlinear characteristics and severe environment interference, it is impossible to extract and quantify exactly these modal parameters or system parameters or indices as the feature vectors of a system in damage detection in an easy way. The SRM considered a more general theory for the non-parametric description of system state.展开更多
For two unequal-mass particles,we construct the entangled state representation and then derive the corresponding squeezing operator.This squeezing operator has a natural realization in the entangled state representati...For two unequal-mass particles,we construct the entangled state representation and then derive the corresponding squeezing operator.This squeezing operator has a natural realization in the entangled state representation,which exhibits the intrinsic relation between squeezing and quantum entanglement.This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings.The maximum squeezing occurs when the two particles possess equal mass.When the two particles＇ mass difference becomes large,the component of the two single-mode squeezings becomes dominant.展开更多
We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by U...We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.展开更多
By introducing the thermo entangled state representation, we derive four new photocount distribution formulas for a given light field density operator. It is shown that these new formulas, which are convenient to calc...By introducing the thermo entangled state representation, we derive four new photocount distribution formulas for a given light field density operator. It is shown that these new formulas, which are convenient to calculate the photocount, can be expressed as integrations over a Laguree Gaussian function with a characteristic function, Wigner function, Q-function and P-function, respectively.展开更多
Based on the Husimi operator in pure state form introduced by Fan et al,which is a squeezed coherentstate projector,and the technique of integration within an ordered product (IWOP) of operators,as well as the entangl...Based on the Husimi operator in pure state form introduced by Fan et al,which is a squeezed coherentstate projector,and the technique of integration within an ordered product (IWOP) of operators,as well as the entangledstate representations,we obtain the Husimi functions of the excited squeezed vacuum states (ESVS) and two marginaldistributions of the Husimi functions of the ESVS.展开更多
We show that the Susskind-Glogower phase state is a limiting case of a kind of SU（1,1） coherent states. By analogy, based on the bipartite entangled state representation （ESR） we demonstrate that an appropriate SU...We show that the Susskind-Glogower phase state is a limiting case of a kind of SU（1,1） coherent states. By analogy, based on the bipartite entangled state representation （ESR） we demonstrate that an appropriate SU（1,1） coherent state composed of the two-mode unitary phase operator e^i also leads to a new phase state in two-mode Fock space, e^i is diagonalized in the ESR.展开更多
In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are investigated.Using the entangled state representation and Weyl ordering formof the W...In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are investigated.Using the entangled state representation and Weyl ordering formof the Wigner operator,the Wigner functions of TDESVS are obtained and the variations of Wigner functions withthe parameters m,n and r are investigated.Besides,two marginal distributions of Wigner functions of TDESVS areobtained,which exhibit some entangled properties of the two-particle's system in TDESVS.展开更多
By virtue of the Weyl correspondence and based on the the technique of integration within an ordered product of operators, we show under what condition the superoperator＇s Kraus representation p^1=∑μAμpA^＋μ can ...By virtue of the Weyl correspondence and based on the the technique of integration within an ordered product of operators, we show under what condition the superoperator＇s Kraus representation p^1=∑μAμpA^＋μ can be deformed as p＇= （1/π） ∫ d^2d^2α（α）D（α）D（α）pD^＋（α）, where D（α） is the displacement operator, B（α） is a probability density related to the classical Weyl correspondence of Aμ. An alternate discussion by using the entangled state representation and through a quantum teleportation process is also presented.展开更多
Based on thermo field dynamics （TFD） and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature （named thermo number state...Based on thermo field dynamics （TFD） and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature （named thermo number states）. The figure of Wigner function shows that its shape gets smoothed as the temperature rises, implying that the quantum noise becomes larger.展开更多
文摘We present the continuous state vector of the total coordinate of multi-partlcle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product （IWOP） technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.
文摘We mostly investigate two schemes. One is to teleport a multi-mode W-type entangled coherent state using a peculiar bipartite entangled state as the quantum channel different from other proposals. Based on our formalism,teleporting multi-mode coherent state or squeezed state is also possible. Another is that the tripartite entangled state is used as the quantum channel of controlled teleportation of an arbitrary and unknown continuous variable in the case of three participators.
基金Project supported by the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Natural Science Foundation of Liaocheng University (Grant No. X071049)
文摘This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state representations seem to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.
基金The project supported by National Natural Science Foundation of China and the President Foundation of the Chinese Academy of Sciences
文摘With the help of Bose operator identities and entangled state representation and based on our previous work.[Phys. Lett. A 325 （2004） 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.
基金Project supported by the National Natural Science Foundation of China(Grant No.11304126)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20130532)
文摘Based on the fact that the quantum mechanical version of Hankel transform kernel（the Bessel function） is just the transform between ｜q, r〉 and（s, r′｜, two induced entangled state representations are given, and working with them we derive fractional squeezing-Hankel transform（FrSHT） caused by the operator e（-iα）（a1-a-2-＋a-1a-2）e-（-iπa2-a2）, which is an entangled fractional squeezing transform operator. The additive rule of the FrSHT can be explicitly proved.
基金Collaborative Innovation Project of University,Anhui Province(Grant No.GXXT-2022-088).
文摘Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, wesolve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum representation ofits analytical solution. we find that the pure coherent states evolve into the new mixed thermal superposed states in thediffusion channel. Also, we investigate the statistical properties of the initial coherent states and their entropy evolutions inthe diffusion channel, and find that the entropy evolutions are only related to the decay time and without the amplitudes ofthe initial coherent states.
基金Project supported by the Foundation for Young Talents in College of Anhui Province, China (Grant Nos. gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions, China (Grant Nos. 2022AH051580 and 2022AH051586)。
文摘To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.
基金supported by President Foundation of Chinese Academy of Sciences and National Natural Science Foundation of China under Grant Nos. 10775097 and 10874174
文摘By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation （η｜, which can arrange master equations of density operators p（t） in quantum statistics as state-vector evolution equations due to the elegant properties of （η｜. In this way many master equations （respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators） can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p（t） at time t in 〈η｜ representation is proportional to that of the initial po in the decayed entangled state （ηe^-kt｜ representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f（d^2η/π）（η｜ρ〉D（η）, which is different from all the previous known representations.
基金supported by the National Natural Science Foundation of China(Grant Nos.11347026,11147009,and 11244005)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2013AM012 and ZR2012AM004)the Scientific Research Project of Liaocheng,China
文摘Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 112470009)
文摘For the first time we derive the evolution law of the negative binomial state In） （nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.
基金The project supported by the Natural Science Foundation of Heze University of Shandong Province of China under Grant Nos.XY07WL01 and XY05WL01the University Experimental Technology Foundation of Shandong Province of China under Grant No.S04W138
文摘By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. The technique of integration within an ordered product （IWOP） of operators is employed in our discussions.
文摘This paper introduces a new concept of ＂State Representation Methodology （SRM）＂ which is a kind of bridge condition assessment method for structural health monitoring system （SHM）. There are many methods for system identification from the simplicity comparison of damage index to the complicated statistical pattern recognition algorithms in SHM. In these methods, modal analysis and parameters identification or many defined indices are common-used for extracting the dynamic or static characteristics of a system. However, there is a common problem： due to the complexity of a large size system with high-order nonlinear characteristics and severe environment interference, it is impossible to extract and quantify exactly these modal parameters or system parameters or indices as the feature vectors of a system in damage detection in an easy way. The SRM considered a more general theory for the non-parametric description of system state.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10975125)
文摘For two unequal-mass particles,we construct the entangled state representation and then derive the corresponding squeezing operator.This squeezing operator has a natural realization in the entangled state representation,which exhibits the intrinsic relation between squeezing and quantum entanglement.This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings.The maximum squeezing occurs when the two particles possess equal mass.When the two particles＇ mass difference becomes large,the component of the two single-mode squeezings becomes dominant.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10574060 and 10775097)the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07)
文摘We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11047133 and 60967002)the Key Program Foundation of Ministry of Education of China (Grant No.210115)+1 种基金the Research Foundation of the Education Department of Jiangxi Province of China (Grant Nos.GJJ10097 and GJJ10404)the Natural Science Foundation of Jiangxi Province of China (Grant No.2010GQW0027)
文摘By introducing the thermo entangled state representation, we derive four new photocount distribution formulas for a given light field density operator. It is shown that these new formulas, which are convenient to calculate the photocount, can be expressed as integrations over a Laguree Gaussian function with a characteristic function, Wigner function, Q-function and P-function, respectively.
基金Supported by National Natural Science Foundation of China under Grant No.10574060Shandong Province of China under Grant No.Y2008A23Liaocheng University of China under Grant No.X071049
文摘Based on the Husimi operator in pure state form introduced by Fan et al,which is a squeezed coherentstate projector,and the technique of integration within an ordered product (IWOP) of operators,as well as the entangledstate representations,we obtain the Husimi functions of the excited squeezed vacuum states (ESVS) and two marginaldistributions of the Husimi functions of the ESVS.
文摘We show that the Susskind-Glogower phase state is a limiting case of a kind of SU（1,1） coherent states. By analogy, based on the bipartite entangled state representation （ESR） we demonstrate that an appropriate SU（1,1） coherent state composed of the two-mode unitary phase operator e^i also leads to a new phase state in two-mode Fock space, e^i is diagonalized in the ESR.
基金Supported by the National Natural Science Foundation of China under Grant No.10574060Shandong Province of China under Grant No.Y2008A23Liaocheng University of China under Grant No.X071049
文摘In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are investigated.Using the entangled state representation and Weyl ordering formof the Wigner operator,the Wigner functions of TDESVS are obtained and the variations of Wigner functions withthe parameters m,n and r are investigated.Besides,two marginal distributions of Wigner functions of TDESVS areobtained,which exhibit some entangled properties of the two-particle's system in TDESVS.
基金National Natural Science Foundation of China under Grant Nos.10775097,10874174,and 10647133the Natural Science Foundation of Jiangxi Province under Grant Nos.2007GQS1906 and 2007GZS1871the Research Foundation of the Education Department of Jiangxi Province under Grant No.[2007]22
文摘By virtue of the Weyl correspondence and based on the the technique of integration within an ordered product of operators, we show under what condition the superoperator＇s Kraus representation p^1=∑μAμpA^＋μ can be deformed as p＇= （1/π） ∫ d^2d^2α（α）D（α）D（α）pD^＋（α）, where D（α） is the displacement operator, B（α） is a probability density related to the classical Weyl correspondence of Aμ. An alternate discussion by using the entangled state representation and through a quantum teleportation process is also presented.
基金supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘Based on thermo field dynamics （TFD） and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature （named thermo number states）. The figure of Wigner function shows that its shape gets smoothed as the temperature rises, implying that the quantum noise becomes larger.
